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Conference Paper

Kernel PCA and De-noising in feature spaces

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84153

Rätsch,  G
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Mika, S., Schölkopf, B., Smola AJ, Müller K-R, Scholz, M., & Rätsch, G. (1999). Kernel PCA and De-noising in feature spaces. Advances in Neural Information Processing Systems, 536-542.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-E699-C
Abstract
Kernel PCA as a nonlinear feature extractor has proven powerful as a preprocessing step for classification algorithms. But it can also be considered as a natural generalization of linear principal component analysis. This gives rise to the question how to use nonlinear features for data compression, reconstruction, and de-noising, applications common in linear PCA. This is a nontrivial task, as the results provided by kernel PCA live in some high dimensional feature space and need not have pre-images in input space. This work presents ideas for finding approximate pre-images, focusing on Gaussian kernels, and shows experimental results using these pre-images in data reconstruction and de-noising on toy examples as well as on real world data.